EC349 Financial Economics 2022-2023 SET EXERCISE
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EC349 Financial Economics 2022-2023 SET EXERCISE
1. Assume a perfect capital market under certainty and answer the following questions.
a) A single-owner firm faces a two-period planning problem with the transformation curve (K1 + 4)2 + K2(2) = 25 and initial resources equalling 1. Assume the market interest rate is 5%. Work out the firm’s initial wealth maximization problem and illustrate your answer in a diagram. [5 marks]
b) What happens if the market interest rate increases? When does the firm stop borrowing from the capital market in time 1? Explain, calculate, and illustrate your answer on top of the same diagram used in a). [5 marks]
c) Suppose the owner ofthis firm has the utility function of U = c1 with no other income or wealth. Using the same market interest rate of 5% and results from a), work out the utility maximisation problem and illustrate your answer on top of the same diagram. [5 marks]
d) Now a proportional transaction fee is applied when this individual borrows from the capital market for consumption purposes. Assume this percentage is equivalent to the last non-zero digit of your student ID – i.e., if your student ID ends with 7, this means the transaction fee equals 7% of the amount borrowed, and if your student ID ends with 90, then 9%, and if your student ID ends with 300, just take 3%, etc. Work out the utility maximisation problem with this new constraint, explain what happens to optimal choice of c1 and c2, and illustrate your answer on top of the same diagram. [10 marks]
2. Assume you have the following von Neumann-Morgenstern utility function: U(w) = 40000 − (200 − )2 where w denotes wealth measured in pounds.
a) Work out the utility maximisation problem and illustrate the answer in a diagram. [5 marks]
b) Explain what Arrow-Pratt coefficients of absolute risk aversion (ARA) and relative risk aversion (RRA) seek to measure. [5 marks]
c) Find out the values for ARA and for RRA for this utility function. How does the individual’s risk attitude vary with the change of their wealth? [5 marks]
d) Your friend believes that Italy will not win the World Cup while you think that there is a 75% probability that it will. Your friend is willing to pay you x pounds if Italy wins and you pay your friend x pounds if it does not. Your current wealth is £80,000. How much should you bet to maximise your utility? Illustrate in a diagram. [10 marks]
For simplicity and convenience of calculation, suppose there are only one risk-free asset with a return of 5%, and two risky assets, Stock A and Stock B. Information on A and B are summarised in the table below.
|
Stock A |
Stock B |
Expected return (%) |
10 |
8 |
Standard deviation (%) |
20 |
10 |
Correlation |
Use the last two digits of your student ID and divide the number by 100 to get the correlation coefficient. For example, if your ID ends with 85, the correlation coefficient is 0.85. Note: if you ID ends with 00, use the third-last and second-last digits instead to work out the correlation coefficient (e.g., if ending in 300, the coefficient would be 0.3). |
a) Explain the concept of the minimum-variance portfolio (excluding the risk-free asset). Calculate the investment weightings, expected return, and risk of the minimum-variance portfolio of this 2-stock portfolio. Illustrate your answer in a diagram. [5 marks]
b) Now include the risk-free asset. Assume your mean-preference utility function is U (E (p), GP) = E(p) − Gp(2) , where γ is the last digit of your student ID. Explain the concept of the optimal portfolio, calculate the investment weightings, expected return, and risk, as well as the corresponding utility level, of the optimal portfolio. Illustrate your
answer on top of the same diagram used in a). [10 marks]
c) Assume there are no other risky assets. What would be the market portfolio? Calculate expected return and standard deviation for the market portfolio. Illustrate your answer on top of the same diagram. [5 marks]
d) Assume the simple CAPM holds for stocks A and B. What is the beta for your optimal portfolio in b) and for the market portfolio in c)? Illustrate your answer using a security market line. [5 marks]
4. Short essay. There are some problems with the original CAPM model, and various extensions have been developed to address these issues, for example, the Intertemporal CAPM, the International CAPM, the Behavioural CAPM, etc. Choose one extension to focus on. Explain the main idea ofthat extension, and appraise its empirical validity using good-quality references. Word limit for Q4: maximum 800 words, excluding tables, diagrams, equations, direct quotes, and reference list. You must note your word count at the end of your answer. [25 marks]
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First > 80% |
First >70% |
2:1 60 – 69% |
2:2 50 – 59% |
3rd 40 – 49% |
Fail <40% |
Criterion not relevant to assignment |
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Relevance |
Totally relevant to the question set. |
Almost wholly relevant to the question set. |
Largely relevant to the question set. |
For the most part, relevant to the question set; may be some irrelevant digressions. |
Only partially relevant to the question set . |
Largely or wholly irrelevant to the question set. |
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Depth-Detail |
Extensive discussion of the main issues. Excellent knowledge and depth of understanding of relevant theories and concepts. |
Detailed discussion of the main issues. Excellent knowledge and depth of understanding of relevant theories and concepts. |
Clear discussion of main issues. Secure knowledge and good depth of understanding of relevant theories and concepts. |
Identification and some discussion of main issues. Reasonable knowledge and understanding of relevant theories and concepts. |
Significant issues not identified or discussed. Superficial knowledge and understanding shown. |
Shows little or no knowledge and understanding of the main issues. |
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Engagement with Literature and Sources |
Excellent understanding of empirical literature/economic theory/policy used, that have gone much beyond the material taught. |
Excellent understanding of the empirical literature/economic theory/policy used, that have gone beyond the material taught. |
Good understanding of empirical literature/ economic theory/policy used, that have gone beyond the material taught. |
Some understanding of empirical literature/economic theory/policy used, but has not gone much beyond the material taught. |
Limited understanding of the empirical literature/economic theory/policy used, that has not gone beyond the material taught |
Limited or no understanding of empirical literature/economic theory/policy, that has not gone beyond the material taught. |
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Application and Analysis of Evidence and Theory |
Excellent integration of economic theory, empirical literature and policy (where relevant), with critical analysis of literature which has both breadth and depth. |
Excellent integration of economic theory, empirical literature and policy (where relevant), with critical analysis of literature. |
Very good integration of economic theory, empirical literature and policy (where relevant), with some critical analysis of literature. |
Good integration of economic theory, empirical literature and policy (where relevant), although discussion of literature is more descriptive than critical. |
Limited integration of economic theory, empirical literature and policy (where relevant); discussion of literature is more descriptive than critical and/or is limited |
Little or no integration of economic theory, empirical literature and policy (where relevant), and little or no discussion of literature. |
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Structure, style and presentation |
Excellent overall organisation and structure. Excellent links between components giving a very strong and logical flow to the overall argument. |
Excellent presentation, with an effective & |
2022-11-11